Ab initio calculations of MgH2, MgH2:Ti and MgH2:Co compounds

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 5 9 8 – 6 0 8

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Ab initio calculations of MgH2, MgH2:Ti andMgH2:Co compounds

Nikola Novakovic*, Jasmina Grbovic Novakovic, Ljiljana Matovic, Miodrag Manasijevic,Ivana Radisavljevic, Bojana Paskas Mamula, Nenad Ivanovic

Vinca Institute of Nuclear Sciences, P.O. Box 522, 11000 Belgrade, Serbia

a r t i c l e i n f o

Article history:

Received 13 May 2009

Received in revised form

27 October 2009

Accepted 1 November 2009

Available online 27 November 2009

Keywords:

Hydrogen storage

MgH2

Transition metal catalyst

Ab initio calculations

* Corresponding author. Tel.: þ381 113408610E-mail address: [email protected] (N. Nova

0360-3199/$ – see front matter ª 2009 Profesdoi:10.1016/j.ijhydene.2009.11.003

a b s t r a c t

The understanding of hydrogen bonding in magnesium and magnesium based alloys is an

important step toward its prospective use. In the present study, a density functional theory

(DFT) based, full-potential augmented plane waves method of calculation, extended with

local orbitals (FP-APWþlo), was used to investigate the stability of MgH2 and MgH2:TM

(TM¼ Ti and Co) 10 wt % alloys and the influence of this alloying on hydrogen storage

properties of MgH2 compound. Effects of a possible spin polarisation induced in the system

by transition metal (TM) ions were considered too. It has been found that TM-H bonding is

stronger than the Mg–H bond, but at the same time it weakens other bonds in the second

and third coordination around a TM atom, which leads to overall destabilization of the

MgH2 compound. Due to a higher number of d-electrons, this effect is more pronounced for

Co alloying, where in addition, the spin polarisation has a noticeable and stabilising

influence on the compound structure.

ª 2009 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.

1. Introduction A large number of experimental studies established that

Limited energy resources and growing pollution associated

with conventional energy production have stimulated the

search for cleaner, cheaper and more efficient energy tech-

nologies. One promising technology involves hydrogen stored

in metal hydrides. Due to its high hydrogen capacity by weight

(7.6 wt. %), its abundance in the Earth’s crust and its low cost,

MgH2 has been the subject of extensive studies [1–8]. The main

obstacles preventing its commercial applications are its high

thermodynamic stability, high desorption temperature and

low plateau pressure at ambient temperature [1,2]. To over-

come these obstacles and to improve the H absorption/

desorption kinetics, a pronounced and detailed under-

standing of the interactions present in the MgH2 compound

and Mg–H systems in general, is of the utmost importance.

; fax: þ381 113440100kovic).sor T. Nejat Veziroglu. Pu

reaction kinetics of hydrogen in MgH2 strongly depends on

synthesis method and presence of additives [3–15]. For

example, ball milling introduces clusters of defects, which

may assist diffusion of hydrogen, lower the barrier for

nucleation of MgH2, produce mechanical deformation and

metastable phases, modify surfaces, etc. All these effects

generally promote the solid–gas reaction [3–6]. Addition of

metals, metal oxides [7–14], or intermetallic compounds as

catalysts [15], can also enhance absorption and/or release of

hydrogen. Recently, some progress has been reported by

means of ion and ultrasonic irradiation also [16–18]. However,

the electronic aspects of these phenomena have not been

completely resolved yet and a comprehensive insight in

hydrogen bonding with magnesium and its alloys is needed to

ensure their future commercial usage.

blished by Elsevier Ltd. All rights reserved.

mailto:[email protected]

http://www.elsevier.com/locate/he

Fig. 1 – (Left) original unit cell of MgH2, (right) 2 3 2 3 2

primitive supercell used in MgH2-TM calculations.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 5 9 8 – 6 0 8 599

A number of theoretical and computational investigations

of MgH2 and related systems [5, 19–33] have been reported.

Stander and Pacey [19] performed a Born–Mayer type of

calculations of the MgH2 lattice energy assuming that

compound is purely ionic. The obtained energy value was

larger than the experimental one and this discrepancy was

interpreted as indication of a covalent bonding contribution to

MgH2. Noritake et al. [20] confirmed that bonding in MgH2 is

a complex mixture of ionic and covalent contributions. Some

additional information about MgH2 was recently obtained

using vibrational spectroscopy and ab initio calculations [21].

Ab initio calculations of Schimmel et al. [22] suggest that

hydrogen diffuses through the Mg metal phase, jumping

between octahedral and/or tetrahedral interstitials. They have

also demonstrated that for large metallic particles and low

temperatures, hydrogen diffusion through the Mg metal is not

expected to be the limiting factor of H kinetics, unless

hydrogen enters Mg matrix merely via small catalyst particles,

lowering in that way the cross section of the H diffusion

channels. Some other DFT calculations performed to study

the formation and diffusion of H vacancies on MgH2 surfaces

and in the bulk [23] suggest that surface desorption is more

likely reaction rate limiting step than H diffusion. Conse-

quently, finding an effective catalyst which could facilitate H

desorption from the MgH2 surface is crucial for improving its

overall sorption performances.

The transition metals have been used as catalysts for

hydrogen sorption, to support the break up of molecular

hydrogen into atoms and their moving into, or out of, MgH2

[3–6,8,9,11–13]. However, the observed catalytic mechanism is

still not adequately explained. Despite numerous theoretical

simulations taking into account the substitution of Mg in

MgH2 compound and MgH2 clusters with TM atoms [25–29],

a further improvement of the hydrogen kinetics requires a full

knowledge of intrinsic mechanisms by which TM alloying

affects the compound properties.

In this perspective we have performed first principles DFT

electronic calculations of MgH2 and MgH2:TM (TM¼Ti and Co)

systems with 10 wt. % TM. Formation enthalpies of the

systems were calculated to access their stabilities. Details of

electronic structure in particular crystallographic planes were

investigated to resolve the principle interactions in the MgH2

compound and the influences introduced by the incorporation

of TM atoms.

2. Details of calculations

Ab initio calculations were performed using DFT based FP-

APWþlo method as implemented in WIEN2K code [34]. The

exchange-correlation interaction was treated within the

generalized gradient approximation (GGA) parameterised by

Perdew et al. [35].

The MgH2 unit cell shown in Fig. 1 (left) has a tetragonal

symmetry (P42/mnm, group No. 136), lattice parameters

a¼ b¼ 0.4501 nm and c¼ 0.301 nm and the internal parameter

x¼ 0.304 [35]. The Mg atom occupies 2a (0, 0, 0) and the H atom

occupies the 4f (x, x, 0) crystallographic position.

In the 1� 1� 5 supercell used by Shang and Song [26,27]

with preserved initial P42/mnm symmetry, there are 8 Mg, 20 H

and 2 TM atoms, which corresponds to an MgH2: TM alloy of

about 20 mol% of TM. Basis and the central plane of the

supercell are formed entirely of TM and H atoms, thus

enabling a significant overlapping of TM electron wave func-

tions. To reduce the overall TM atoms concentration, we have

used a larger primitive supercell, with 2� 2� 2 stacked orig-

inal MgH2 unit cells and Cmmm symmetry, with TM atoms

placed in the supercell corners (Fig. 1, right). The supercell

contains 15 Mg atoms, 32 H atoms and 1 TM atom

(Mg15TMH32), which corresponds to an alloy with the TM

content of about 10 wt % (specifically: 10.77 wt.% Ti and

12.93 wt.% Co). In addition, TM atoms are now distributed

more regularly throughout the MgH2 matrix.

The proper procedure of structural relaxation involves

synchronized optimisation of the unit cell volume and c/a

ratio and minimization of forces acting on atoms. However,

due to the size and complexity of the supercell, the full

relaxation of this structure is very time-consuming. There-

fore, as the first stage of optimisation we fully relaxed the

MgH2 structure. The unit cell parameters and fraction coor-

dinates from these calculations were used to define the

initial supercell. Assuming that introduction of TM atom

causes only local changes in its first and second coordination

shells, only additional minimization of forces in the super-

cell was carried out.

In all calculations the muffin tin radii (RMT) of Mg, Ti and Co

were 2.13 bohr (1.13 A) and 1.08 bohr (0.57 A) for H. Such

a large RMT difference was compensated with a smaller basis

size cut-off parameter RMTKmax¼ 5.5. 280 k points in the irre-

ducible wedge of the Brillouin zone (IBZ) were used for MgH2

and 18 k points for the supercell calculations. The charge

difference of 10�5 electrons between the two successive

calculations was used as the convergence criterion, since it

ensures better stability of the calculated values than the cor-

responding energy criterion. Core states were treated fully

relativistically, while valence states were treated within scalar

relativistic approximation, with spin-orbit interaction

neglected. To include the low lying TM s-states, the core-

valence states threshold energy was chosen at �6 Ry for Ti

and �8 Ry for Co. d-states above the Fermi level (EF) were

considered using extra local orbitals. To obtain enthalpy of

formation of MgH2, MgH2:Ti and MgH2:Co, we performed

calculations of pure hcp Mg, Co and Ti metals. Parameters

used in these calculations are given in Table 1. 4000 k points in

Table 1 – Parameters used for calculations of pure metals ground state energy.

Element Space group Structure type a [nm] b [nm] c [nm] E [Ryd]

Mg P63/mmc hcp 0.32094 0.32094 0.52108 �801.335

Ti P63/mmc hcp 0.29508 0.29508 0.46855 �3415.250

Co P63/mmc hcp 0.25071 0.25071 0.40695 �5573.874


the entire Brillouin zone were used in all cases. Spin-polarised

calculations were carried out for the Co ferromagnetic ground

state, as well as for the MgH2:Co compound.

3. Results and discussion

3.1. Density of states of pure MgH2

Calculated MgH2 DOS’s are presented in Fig. 2. The obtained

broad energy gap (Eg) of about 3.8 eV, is typical for an insu-

lating system and its value is in fair agreement with the

previously calculated 3.4 eV [31]. The discrepancy between

experimental 5.16 eV [32], or 5.6 eV [33] and theoretical results

Fig. 2 – Total DOS (solid line) of MgH2, with atomic contribution

momentum decompositions of DOS of Mg (solid line) and H (dash

[31] should be attributed to the calculation method and in our

case, also to the choice of the exchange-correlation potential.

The Fermi level is positioned immediately above the valence

band, which is composed mainly of strongly hybridised H-s

and Mg-3p states, with two distinct peaks, the one positioned

approximately�2 eV below and the other just below the Fermi

level. Besides the H-s, the bottom of the valence band

comprises also some Mg-s states, with a maximum at �4 eV.

The bottom of the conduction band (EC) is predominantly of

Mg-p origin, but the Mg-s contribution cannot be neglected

as well.

Various contributions to the valence band DOS of MgH2 are

presented in Table 2. To evaluate the influence of the MT

sphere radii on charge distribution, the results for three

s of Mg (dash line) and H (dash-dot line) and orbital

line) for middle: l [ 0 (s-states) and bottom: l [ 1 (p-states).

Table 2 – The MgH2 valence band DOS structure close to the Fermi level.

MT-radius [A] Acc* Mg[e/atom]

Mg-s[e/atom]

Mg-p[e/atom]

H[e/atom]

H-s[e/atom]

H-p[e/atom]

Interstitial charge[e/unit cell]

Mg H

1.13 0.57 8.00 0.5881 0.2331 0.2602 0.6677 0.6636 0.0037 4.19

0.85 0.85 8.00 0.1348 0.0586 0.0622 1.0080 0.9935 0.0126 4.05

0.64 1.06 8.00 0.0616 0.0223 0.0363 1.3438 1.3020 0.0339 3.85

Acc* – accumulated or total number of electrons in the valence band, per unit cell.

Fig. 3 – Valence electron charge densities in [110] (upper)

and [100] (lower) crystal planes of the MgH2 unit cell.


different sets of Mg and H MT radii are presented. Both atomic

and l decomposed values are given for the charge enclosed

within the MT spheres and per atom. Depending on the MT

sphere radii set used, the amount of the interstitial charge

varies between 3.85 and 4.19 e/unit cell (0.69 e/at.). This is the

consequence of the fact that the sum of volumes of all MT

spheres inside the unit cell is only 27–35% of the total unit cell

volume. The observed large spatial extension of H� ions and

the fact that some of the interstitial charge clearly originates

from Mg atoms, tell us that both atoms contribute to the large

interstitial charge, although through different mechanisms.

In pseudopotential calculations of MgH2, Yu et al. [32]

determined ionic radii assuming that nearest neighbour (NN)

ions are in immediate contact with each other and found

values of 0.6 A and 1.26 A for Mg and H, respectively. The ionic

charges calculated using these radii are 2þ for Mg and 0.6� for

H, providing a picture of an almost purely ionic compound and

the interstitial charge is 1.6 e/unit cell. Trends of the charge

confined inside the Mg and H MT spheres, presented in Table

2, go toward results of [32] and known empirical relations

between the ionic radii of Mg and H and their charge states

[20]. Obviously, in MgH2, the choice of a particular MT radius

significantly influences the amount of charge it confines and it

must be carefully handled to provide a reliable physical

picture of the charge distribution in the compound.

Calculations of the hypothetical compound consisting of H

atoms alone, placed at same lattice positions as in original

MgH2 [32], provided energy bands similar to those of MgH2, but

with a narrower valence band and a significantly larger energy

gap (around 5 eV). This is easy to understand in the light of our

calculations, which impart that structure of the valence band

is determined by a strong Mg-H hybridisation and that the

bottom of the conduction band is predominantly of Mg-

character.

Valence charge densities in [110] (above) and [001] (below)

crystallographic planes are presented in Fig. 3. In the [110]

plane two interesting features should be pointed out. Mg

atoms are strongly charge depleted (although less than pre-

dicted in [32]), but unlike in a typical ionic compound, this

‘‘borrowed’’ charge is not completely located at distinct H

ions, but shared between the two neighbouring H’s promoting

a resonant bonding between them. This feature is visible also

in the [001] plane. Despite the fact that the small distance

between the NN H atoms results in a fairly large overlap of

their orbitals, which is one of the reasons for the observed

complexity of the MgH2 electron bands, the charge density

contour plots in Fig. 3, as well as in Fig. 6 of [32], do not support

the assumption that observed resonant bonding is of the

covalent type. The remaining valence charge delocalised from

Mg is spatially extended toward its next nearest neighbours

(NNN) Mg atoms. A part of this charge is ‘‘squeezed’’ between

its four NN H’s and a part is located in the ring formed of four

Mg and four H ions. Such a charge distribution and the

amount of calculated interstitial charge (Table 2), suggests

that besides a dominant MgeH ionic contribution, the HeH

(and perhaps even the MgeMg) bonding contribution to the

compound stability is not negligible.

3.2. MgH2 with Ti and Co impurities

3.2.1. DOS of MgH2:Ti systemTotal and atomic densities of states of Ti and its surrounding

atoms in MgH2:Ti are presented in Fig. 4. The main difference

from the pure MgH2 DOS is the existence of two prominent

Ti-d states peaks. However, due to the s–d and p–d hybrid-

isation, s and p states in the compound are also affected, but in

a different way for different Ti neighbours. The lower energy

Ti-d peak is placed in the vicinity of the centre of the energy

gap of pure MgH2. It determines the position of the MgH2:Ti

Fermi level and provides a high density of states at the Fermi

level. The second Ti-d peak is positioned at the bottom of the

conduction band of pure MgH2. In such a way, these quasi-

localised Ti-d states, makes the Eg of MgH2:Ti considerably

smaller than that of pure MgH2, in the manner that resembles

Fig. 4 – Total DOS of (top to bottom): MgH2:Ti, atomic DOS of Ti, atomic DOS of Ti NN Mg and of the two non-equivalent NN H

atoms in the first coordination octahedron of Ti.


a highly doped semiconductor. Although both Ti-d peaks are

narrow, which indicates their small overlap with states of

neighbouring atoms, their influence is visible in DOS’s of Ti Mg

neighbours and to a smaller extent in DOS’s of both types of

non-equivalent NN H atoms, meaning that some of Ti-

d charge is redistributed to its neighbours. Despite an evident

influence of Ti-d states on both the valence and conduction

bands, the general MgH2:Ti DOS features, not directly related

Fig. 5 – Orbital momentum decomposition (l [ 0, 1, 2 correspond to columns 1, 2 and 3 respectively) of atomic DOS for: Ti

(top), Ti NN Mg (second row) and two non-equivalent NN H atoms (bottom rows).


to Ti-d states, are similar to those in pure MgH2. The contri-

bution of Ti-s and Ti-d states deeper in the valence band is

more prominent at H4, than at H2 site, reflecting the spatial

distribution of Ti states.

More details about the impact of particular Ti states on its

neighbours can be deduced from the orbital momentum

charge decomposition of atomic DOS’s of MgH2:Ti, presented

in Fig. 5. As mentioned above, the dominant Ti contribution to

the total DOS comes from its 3d states, placed at Fermi level

and at bottom of conduction band. But, the Ti influence exists

deeper in the valence band as well. The influence in the region

around �4 eV comes from Ti-d:H-s hybridisation, which is

stronger with H4 than H2 neighbours and a Ti-d:Mg-p

hybridisation. The influence taking part between �5 and

�6 eV is mostly a consequence of Ti-s:Mg-s hybridisation.

However, the genuine Ti-s and Ti-p contributions to the total

DOS of MgH2:Ti are smaller than the corresponding H-s or Mg-

p contributions. Presence of the Ti states deep in the valence

band and their extension to other atomic positions implies

that Ti takes part in resonant bonding present in MgH2.

The Ti-d:H-p hybridisation, taking place in the energy

range around EF and the bottom of conduction band at both

non-equivalent H positions is much weaker than the Ti-d:H-s

hybridisation present in valence band. On the other side, Ti-

d:Mg-p and Ti-d:Mg-s interactions are of a similar strength.

Also, the Ti-d:Mg-p hybridisation is stronger than the Ti-d:H-p

one, which looks like more of an extension (both in energy and

real space) of Ti-d to H-p states, than an authentic electronic

interaction.

3.2.2. MgH2:Co systemTo compare influence of a transition metal with a nearly

empty d-band (Ti) and the one with an almost full d-band (Co)

on MgH2 properties and to figure out the importance of Co spin

polarisation in that process, we performed both spin non-

polarised (SNP) and spin polarised (SP) calculations of

MgH2:Co. Our calculations show that the spin polarised solu-

tion is energetically preferred (see Table 3), so these results are

used in further discussions.

Total and atomic DOS’s obtained by SP calculations of

MgH2:Co are presented in Fig. 6. In Fig. 6 (left) spin-decom-

posed DOS’s are shown, with positive part of Y-scale corre-

sponding to ‘‘spin-up’’ and negative part of Y-scale to ‘‘spin-

down’’ states. The sum of ‘‘spin-up’’ and ‘‘spin-down’’ DOS’s

are shown in Fig. 6 (right). The presented DOS differs from

pure MgH2 more than that of MgH2:Ti, implying stronger

Fig. 6 – Spin-decomposed (left column) and spin-summed (right column) densities of states of MgH2-Co system. (Top to

bottom) total DOS, atomic DOS of Co, atomic DOS of Co NN Mg and of the two NN non-equivalent H.


interaction of Co impurity with the native MgH2 compound.

The main common characteristics of MgH2:Co and MgH2:Ti

DOS’s is existence of large, narrow and localised d-peaks. The

most obvious difference between the SP MgH2:Co and

the MgH2:Ti DOS, is a spin splitting of the Co-d states, making

the d-band considerably wider and particular peaks much

lower than in the SNP case. Four ‘‘spin-up’’ and four ‘‘spin

down’’ peaks appear, with ‘‘spin down’’ states shifted toward

higher energies. These peaks introduce spin polarisation in

total DOS of MgH2:Co, mainly in the valence band, around EF

and at the bottom of the conduction band. However, spin

polarisation is almost completely absent from the rest of the

conduction band.

This redistribution of Co-d states makes the intrinsic Eg

narrower (z3 eV) than in pure MgH2 and the gap between the

Table 3 – Calculated results of structural optimisation, total enMgH2:Co. Result of spin non-polarised calculations of MgH2:Co

Compound Distances [A]

Central atom 4H 2H 2M

MgH2 Mg 1.952 1.953 3.0

MgH2:Ti Ti 1.916 1.905 3.0

MgH2:Co Co 1.789 1.802 3.0

d-peaks at EF and at bottom of conduction band is only z1 eV.

Another direct consequence of the Co 3d states spin-splitting

is much lower number of states at Fermi level (5 states/(eV

unit cell) instead of nearly 20 states/(eV unit cell) obtained for

the SNP case) and a much larger number of states in the much

wider valence band, leading to a significant structural stabi-

lisation of the compound. Two large d-peaks in the middle

(�4 eV) and close to the bottom of the valence band (�7 eV) are

absent from the MgH2:Ti and the SNP MgH2:Co DOS’s. They are

visible at all Co NN atomic sites, suggesting their strong

hybridisation with Mg and H states.

DOS decomposition by orbital momentum for all atomic

sites of interest in the MgH2:Co system is presented in Fig. 7. A

strong spin polarisation induced by the magnetic contribution

of Co d-states is present at all crystallographic positions. Co

ergies, and heats of formation, of MgH2, MgH2:Ti, andis given in parenthesis.

Etot [Ryd] DH [kJ/molH2]

g 4H

19 3.424 �806.084 �69.51

41 3.440 �7755.533 �60.64

25 3.458 �8834.792 (�8834.720) �53.23

Fig. 7 – Orbital momentum decomposition (l [ 0, 1, 2 correspond to columns 1, 2 and 3 respectively) of spin polarised MgH2-

Co atomic densities of states: Co (top), Co nearest neighbour Mg (second row) and of the two non-equivalent Co nearest

neighbour H atoms (the two bottom rows).


d-electrons in vicinity of Fermi level participate more in the

interactions with other atoms, than electrons at lower energy,

that stay more localised around Co atomic position.

The Co-s peak at the bottom of the valence band visible at

all atomic positions is in the first place the consequence of

a strong s–d hybridisation at Co atom itself. It is approximately

of same intensity at Mg and H2 sites and weaker at the H4 site.

The opposite is true for the s-peak close to the EF, which is

highest at the H4 position and weakest at NNN Mg site.

Generally, in MgH2:Co, like in MgH2:Ti, Co-H interaction is

stronger than the Co-Mg one. Consequently, H atoms placed

around central Co are more influenced by spin polarisation

than more distant Mg atoms. Also, at both H atoms, the s–

d hybridisation is much stronger than the p–d one and they are

of comparable magnitude at the Mg site, similar as in MgH2:Ti.

3.3. Charge density distributions in MgH2:Ti andMgH2:Co systems

The valence charge densities in [�1�10] (left) and [110] (right)

planes of MgH2:Ti are presented in Fig. 8. Upper images

correspond to the charge of the complete valence band, while

lower images represent the charge of the isolated narrow Ti-

d peaks positioned near the Fermi level. Spin decomposed

charge density in these two planes in MgH2:Co is presented in

Fig. 9 (entire valence band) and Fig. 10 (Co-d peaks in vicinity of

Fermi level). In all three figures, TM atoms are situated in the

middle of the planes. Two of six NN H atoms forming an

octahedron around a central TM atom are visible in [�1�10]

and four in [110] plane.

The valence charge features of the TM doped compounds

are quite different from these of the pure MgH2 compound

presented in Fig. 3. Strong bonding of TM atom with the

surrounding H atoms octahedron, expressed in a significant

amount of shared charge in both planes, is absent from the

similar MgeH configuration in MgH2. In [�1�10] plane the

charge distribution is extended from TM NN H atoms to those

H’s belonging to third TM neighbours in this plane, making

a connected, five atoms HeHeTMeHeH line-cluster. In the

[110] plane the five atom TMeH cluster is of a quadratic form.

These pictures are quite different from this in MgH2

compound, presented in Fig. 3, where the Mg non-bonding

Fig. 8 – Charge density distributions in [110] (left) and [L1L10] (right) plane of MgH2-Ti. Ti atom is positioned at the center.

Upper images represent the charge distribution of the entire valence band, lower images the charge distribution of localised

Ti d-peak in the vicinity of the Fermi level.


charge is ‘‘squeezed’’ between the two neighbouring H

‘‘molecules’’, separating them from each other.

Electronic charge distributions of the narrow d-bands near

the Fermi level are presented in lower images of Fig. 8, for

MgH2:Ti and in Fig. 10, for MgH2:Co. Despite the fact that the

most of the d-charge is still localised near the TM atom, it is

obvious that the charge of the narrow d-peaks is distributed

not only on TM and surrounding H atoms, but also to more

distant atoms, including both NNN H and Mg. This feature is

visible also in DOS’s presented in Figs. 4–7. Without a strong

hybridisation with electron functions of neighbouring atoms,

TM-d charge should sharply decrease with distance from a TM

Fig. 9 – Charge density distributions in [110] (left) and [L1L10] (

positioned at the center. Upper images correspond to spin-up a

atom. This extension of d-charge is more pronounced around

Co than around a Ti atom, a consequence of different elec-

tronic structure of their d-bands. Only two electrons initially

populate Ti-3d states and they are directed in space between

surrounding H atoms, leaving the bonding Ti-H directions

depleted, as it is clearly visible in Fig. 8. On the other hand, Co

initially has seven electrons populating 3d states, providing

almost spherical charge distribution around Co. This charge

distribution is more abundant and directed toward NN H

neighbours, providing a stronger Co-H bonding, expressed in

shorter Co-H than Ti-H distances (Table 3). This difference of

spatial charge distribution in the vicinity of Ti and Co ions is

right) plane of MgH2-Co, of entire valence band. Co atom is

nd lower images to spin-down states.

Fig. 10 – Charge density distributions in [110] (left) and [L1L10] (right) plane of MgH2-Co, of localised states in the vicinity of

the Fermi level. Co atom is positioned at the center. Upper images correspond to the spin-up states and lower to spin-down

states.


probably enhanced by the effect of crystal field splitting,

partially lifting degeneracy of 3d states [36].

There are some other interesting and unusual features of

TM bonding with the immediate H neighbours, with conse-

quences on overall structure stability. Although the TM-H

distances are quite short, the charge distribution shows that

TM-H bonds are not of the covalent type. Instead, TM atoms

provide the charge which is shared by its first H neighbours. In

the [�1�10] plane, this charge is even extended to two

hydrogen atoms in the third coordination shell, aligned with

Ti and its two NN H atoms. In both [110] and [�1�10] plane,

number of atoms connected in that way is five, one TM and

four H’s, but their spatial arrangement is different. In [110] it is

quadratic, while in [�1�10] it is linear, with the TM atom in

the middle in both cases. Further extension of this charge in

both planes is prevented by NNN Mg atoms. At the same time,

the MgeH and HeH bonds of the atoms surrounding these

clusters are weakened, making the overall stability of the

compounds with TM impurities lower. This is in direct rela-

tion to the strength of TMeH bonding, which is visible from

calculated enthalpies of formation (Table 3). All these findings

are in a good accordance with results of ab initio cluster

calculations of [29], where similar trends for TM-d band filling

and TM bonding are obtained, implying that ‘‘cluster’’ effects

are present already in the bulk of MgH2:TM systems.

4. Conclusions

We performed first principle electronic structure calculations

of pure MgH2 and MgH2 with approximately 10 wt.% of Ti and

Co impurities.

In addition, both spin-polarised and non spin-polarised

calculations of MgH2:Co were performed, to take into account

a possible magnetic influence of Co impurity on the MgH2:Co

properties. Our calculations show that the spin-polarised

solution is more stable and that the energy of magnetic

ordering is about 1 eV per primitive cell. The spin polarisation

influences electronic structure of MgH2:Co by different extent

of hybridisation of ‘‘spin-up’’ and ‘‘spin-down’’ states with

neighbouring H and Mg atoms. Spin polarisation also changes

the width of the compound valence band and changes the

position of the Fermi level and the width of the energy gap.

It appears that introduction of both TM impurities desta-

bilise the native MgH2 structure. This destabilization is more

pronounced in the Co case. Destabilization is induced by

a specific interaction of the TM atoms with their immediate H

neighbours, resulting in formation of tightly bounded nine

atom clusters, consisting of a central TM and four H atoms in

both [110] and [�1�10] plane. The resulting structure is an

octahedron of H atoms around TM, with two additional H

atoms connected above and below the octahedron in the

[�1�10] plane. Electronic distribution inside these clusters

depends on the electronic structure of the TM impurity. It is

denser and more homogenous for Co than for Ti. Conse-

quently, the Co-H clusters are stronger bonded than the cor-

responding Ti clusters. Charge localisation inside the clusters

around TM and the strong bonding existing in them, produces

weakening of bonds on atoms in the cluster vicinity. This

makes the overall structure of the compound less stable in

proportion to the amount of charge located inside the clusters.

Calculated heats of formations go in favour of a such

conclusion, providing a decrease of the compounds stability in

order MgH2>MgH2:Ti>MgH2:Co. These results suggest that

the uptake and release of H atoms that are not directly

bounded to the TM clusters is easier (faster and at lower T) in

the reverse order MgH2:Co>MgH2:Ti>MgH2. However,

release of H’s that are tightly bounded in TM clusters will be

slower and at higher T than in pristine MgH2. Obviously,

a careful optimisation, which should include type,


concentration and spatial distribution of TM impurities in the

MgH2 crystal lattice is necessary to achieve the hydride with

desired H kinetics.

Acknowledgment

This work is financially supported by the Ministry of Science

and Technological development of Republic of Serbia under

project 141009 and 142027.

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Ab initio calculations of MgH2, MgH2:Ti and MgH2:Co compounds

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